Optimal selling rules for monetary invariant criteria: tracking the maximum of a portfolio with negative drift,

Article, Preprint English OPEN
Elie, Romuald; Espinosa, Gilles-Edouard;
(2012)
  • Publisher: HAL CCSD
  • Journal: Mathematical Finance (issn: 0960-1627)
  • Publisher copyright policies & self-archiving
  • Identifiers: doi: 10.1111/mafi.12036
  • Subject: Optimal stopping | Optimal prediction | 93E20, 60H30, 60J75 | Free boundary PDE | Running maximum | [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] | Mean reverting diffusion | Verification

Considering a positive portfolio diffusion $X$ with negative drift, we investigate optimal stopping problems of the form $$ \inf_\theta \Esp{f\left(\frac{X_\theta}{\Sup_{s\in[0,\tau]}{X_s}}\right)}\;,$$ where $f$ is a non-increasing function, $\tau$ is the next random t... View more
  • References (4)

    [1] M. Dai, H. Jin, Y. Zhong and X. Zhou (2010). Buy low and sell high. Contemporary Quantitative Finance: Essays in Honour of Eckhard Platen, C Chiarella & A. Novikov Editors, , 317-334.

    [2] J. Du Toit and G. Peskir (2007). The trap of complacency in predicting the maximum. Ann. Probab. 35, 340-365.

    [3] J. Du Toit and G. Peskir (2008). Predicting the time of the ultimate maximum for Brownian motion with drift. Proc. Math. Control Theory Finance (Lisbon 2007), 95-112, Springer Berlin.

    [4] J. Du Toit and G. Peskir (2009). Selling a stock at the ultimate maximum. Ann. Appl. Probab. 19 (3), 983-1014.

  • Similar Research Results (1)
  • Metrics
Share - Bookmark